An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

Let $X = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : \frac{x^2}{8} + \frac{y^2}{20} < 1 \text{ and } y^2 < 5x\}$. Three distinct points $P, Q,$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q,$ and $R$ form a triangle whose area is a positive integer is

$A$ drawer contains $5$ brown socks and $4$ blue socks well mixed. $A$ man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match?

$A$ cricket team has $15$ members,of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ are drawn at random,then the probability of obtaining a team of $11$ containing at least $3$ bowlers is

If three smallest squares are chosen at random on a chess board, then the probability of getting them in such a way that they are all together in a row or in a column is

If three dice are thrown,then the probability that the sum of the numbers on the uppermost faces is at least $5$ is: